Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 15, Number 1 (2015), 371-397.
The Ptolemy field of $3$–manifold representations
The Ptolemy coordinates for boundary-unipotent –representations of a –manifold group were introduced by Garoufalidis, Thurston and Zickert [arXiv:1111.2828] inspired by the –coordinates on higher Teichmüller space due to Fock and Goncharov. We define the Ptolemy field of a (generic) -representation and prove that it coincides with the trace field of the representation. This gives an efficient algorithm to compute the trace field of a cusped hyperbolic manifold.
Algebr. Geom. Topol., Volume 15, Number 1 (2015), 371-397.
Received: 21 January 2014
Revised: 9 May 2014
Accepted: 7 July 2014
First available in Project Euclid: 16 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57M27: Invariants of knots and 3-manifolds
Garoufalidis, Stavros; Goerner, Matthias; Zickert, Christian. The Ptolemy field of $3$–manifold representations. Algebr. Geom. Topol. 15 (2015), no. 1, 371--397. doi:10.2140/agt.2015.15.371. https://projecteuclid.org/euclid.agt/1510840915